The equation of a circle $C$ is $x^2+y^2-16x+2y+61 = 0$. What is its center $(h, k)$ and its radius $r$ ?
To find the equation in standard form, complete the square. $(x^2-16x) + (y^2+2y) = -61$ $(x^2-16x+64) + (y^2+2y+1) = -61 + 64 + 1$ $(x-8)^{2} + (y+1)^{2} = 4 = 2^2$ Thus, $(h, k) = (8, -1)$ and $r = 2$.